Some of these are on mobile or under emulators, and are thus, free! Some of them are a bit combat'y, but nice slow strategic combat, no real twitch reflexes needed.
M. U. L. E. (NES). OK, it's not that slow paced (everything is realtime), but it's not fast either. Business/resource sim where you try and out-compete your opponents by getting monopolies on various resources and selling during a market crash or random boom. An oldie but a goody.
FreeCol/Colonization (PC/mobile version doesn't work for me). Turn-based Civ-like where you conquer the new world. Half trading game, but with a bit of war thrown in at the end. Extra civs in the freeCol version (Russian fur trapping is crazy strong), but quite balanced otherwise. Be nice to the natives.
OpenTTD (PC, also on mobile but kinda hard to play). The transportiest train simulator you could ever want. Transport Tycoon is great. Rail doesn't really make that much money compared to air travel, but it's the fun part. Signals are an artform.
FreeCiv (PC/mobile). Just like Civ1/2, but free, and you can start with an explorer, so the early game isn't boring. Still nice and simple though, yet can be challenging at the same time.
Pirates! (NES). Float around the place capturing ships and looting towns, and in theory rescuing your family. The NES version has a very simple, quick menuing system and no dancing what-so-ever. Go for navigation, so you're faster than most other ships, for a relaxing time of it. Swordfights aren't too fast until the highest difficulty either.
Ghengis Khan 2 (SNES). Once you figure out what all the little symbols mean (read a FAQ), it's like mini-EUIV/CK2, but turn based. You can sort of turn your brain off while you conquer the known world and marry your daughters off to despondent generals. Can play it without combat turned on if you'd like.
Templar Battleforce (mobile). A mixture between Laser Squad/Xcom original and WH40k. Turn-based, enjoyable carnage, that never gets into Space Hulk levels of situational stress. You can also respec anyone to whatever in between missions, so you can't make wrong decisions on level ups (maybe on squad member purchasing, but not really). Satisfyingly strategic.
Stick Ranger (PC/mobile). Umm, it's an RPG party simulator, where your group kind of wanders along by themselves, you've just got to move them into the correct positions on a semi-regular basis. Later levels can be a bit rock/paper/scissors on what equipment will work, but overall it's simple and relaxing and enjoyable to watch/play.
Underhand (mobile and maybe PC). A mixture between Reigns and a cult simulator in card game format. More-or-less just resource management and understanding objectives, but with some very funny writing, scenarios and ways of completing missions.
The Incredible Machine (dosbox, works well on mobile). One of the original puzzle games, and still fun to this day. Work your brain in a non-timebased way. Rube Goldberg machines aplenty. Has sequels for more puzzles if you want.
Merchant Prince (dosbox). Trading with a bit of politics. Can get a bit boring, but you can also be Doge or the Pope. I liked it.
Settlers (dosbox). Kind of slow, but cutesy and very charming. Resource/supply chain simulator. Works well on mobile if you can setup a right-click function under Magicdosbox or something.
Lords of the Realm (dosbox). Conquer England with an invincible army of Irish Spearmen. Or, manage fields and build castles. Kind of micromanagement intensive each turn for best results, but also a good way of relaxing. Combat is slow and fairly non-strategic, castles can be min-maxed to hell, and once you've got some mercenaries you kind of just win. I still enjoy it though.